Testing Kak's Conjecture on Binary Reciprocal of Primes and Cryptographic Applications

TL;DR

This paper investigates the binary and ternary representations of prime reciprocals, confirming a conjecture that zeros exceed ones in most cases up to one million, and explores cryptographic applications of these findings.

Contribution

It provides empirical evidence supporting Kak's conjecture for primes less than one million in binary and ternary forms, and discusses potential cryptographic uses.

Findings

Zeros exceed ones in binary prime reciprocals up to one million.

Similar results observed in ternary representations.

Potential cryptographic applications discussed.

Abstract

This note considers reciprocal of primes in binary representation and shows that the conjecture that 0s exceed 1s in most cases continues to hold for primes less one million. The conjecture has also been tested for ternary representation with similar results. Some applications of this result to cryptography are discussed.